Vibratory seismic sources, typically referred to as seismic vibrators, are commonly used in connection with the acquisition of seismic data, such as vertical seismic profiling (VSP) data. A seismic vibrator is a low-impact (low amplitude), typically hydraulic, source programmed to generate a signal within a certain frequency range. The source's signal has a duration of several seconds, typically around 10 seconds, during which time the driving signal of the vibrator continuously changes from a minimum value, e.g. 8 Hertz, to a maximum value, e.g. 100 Hertz. The long signature is typically condensed to an approximate impulse by correlating the acoustic signals recorded by the seismic receivers with a reference signal, typically a recording of the synthetic sweep used to drive the vibrator. The correlated traces are typically truncated to a reasonable length, often to between 2 and 4 seconds, before further processing is done.
One commonly seen problem with seismic vibrators is that the response of the vibrator is non-linear such that the vibrator, in addition to the acoustic signal at the intended frequency, sends out energy at higher harmonics, or multiples of this frequency. For an upsweep signal (starting at low frequencies and ending at high frequencies) the harmonic energy represents a too-early occurrence of the higher frequencies. In the VSP context, when the recordings of the down-hole receivers are correlated with a reference signal that does not contain a proper description of this harmonic energy, the result is an asymmetric signal with the harmonic energy leading the main energy burst by a time determined by how much too early the (e.g. 60 Hertz) signal occurred. This lead-time may be several seconds for the higher frequencies, leaving some of the energy outside the time window saved for further processing, typically the part associated with the signal directly transmitted from the source to the receiver. However, the correlated section of data will contain improperly placed energy all over, mostly at higher frequencies, eventually limiting the useful bandwidth of the data. In addition to this, the correlated data will be limited to the same frequency band as the reference signal. The production of harmonic energy by seismic vibrators is typically difficult to predict and difficult to measure.
Other factors can also produce differences between the actual force imparted into the ground by a seismic vibrator and the signal intended to be imparted. Flexing of the vibrator base plate and variable ground coupling, for instance, can produce changes in the source signature other than harmonics.
At least two methods for attempting to address these types of differences are known. In one method, taught in U.S. Pat. Nos. 4,646,274, 5,550,786, 5,570,833, 5,715,213, and 5,721,710, one or more sensors are mounted to the vibrator (typically on the vibrator's baseplate) and signals from these sensors are used to estimate the actual source signature imparted by the vibrator. This estimate of the actual source signature is then used instead of the reference sweep to produce the correlated traces. While this type of method can offer significant advantages compared to the use of the reference sweep, this type of method typically does a less than perfect job of estimating the source signature actually imparted into the earth by the vibratory seismic source because a sensor mounted on the vibrator can only sense the outgoing seismic wavefield indirectly.
A second type of method, as taught for instance in WO2004031806 A2, involves attempting to quantitatively estimate the “noise” (i.e. the difference between the desired reference signal and the seismic signal actually imparted by the vibrator, such as harmonics) and then subtracting the transmitted “noise” from the received seismic signals. In practice, however, it is often very difficult to clearly distinguish between “noise”, which one would like to remove from the data, and “signal” which must to be substantially retained to allow the subsurface to be adequately characterized.
For these reasons, it would be of great benefit to be able to process seismic data obtained from the use of a vibratory seismic source in a way that appropriately addresses the differences between the desired and actual source signatures and is able to use these differences in source signature, such as harmonics, as signal rather than noise to the maximum extent possible.